where \(P_\varepsilon =(1-\varepsilon )P+\varepsilon \delta _x\) 
and we have, from [1]} that
\(IF(x)=M^{-1}\frac{x}{\Vert x\Vert }\psi (\Vert x\Vert ),\) 
where
\(M=-\mathbb {E}\left[\left(\frac{I_d}{\Vert X\Vert }-\frac{XX^T}{\Vert X\Vert ^3} \right)\psi (\Vert X\Vert )+\frac{XX^T}{\Vert X\Vert ^2}\psi ^{\prime }(\Vert X\Vert ) \right] .\) 
